Know What You Don't Know: Uncertainty Calibration of Process Reward Models
This work addresses calibration issues in PRMs for LLMs, enabling more efficient inference in mathematical reasoning, but it is incremental as it builds on existing scaling algorithms.
The paper tackles the problem of poorly calibrated process reward models (PRMs) in large language models, which overestimate success probabilities, and presents a calibration method via quantile regression that reduces calibration error and enables an instance-adaptive scaling framework to reduce inference costs while maintaining accuracy.
Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated. Specifically, they tend to overestimate the success probability that a partial reasoning step will lead to a correct final answer, particularly when smaller LLMs are used to complete the reasoning trajectory. To address this, we present a calibration approach -- performed via quantile regression -- that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an \emph{instance-adaptive scaling} (IAS) framework that dynamically adjusts the compute budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective IAS, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.